Registration and comparison of three-dimensional objects

ABSTRACT

Information of different scans of physical objects may require comparison, for example to determine if the scans are of the same object or if an object has changed, or better information for a three dimensional model may be desired. Different scans of physical objects may be compared by determining lines or planes tangent to a surface at a discrete number of points, registering three dimensional information provided by the scans using the tangent lines or planes, and determining a measure of discrepancy between the surfaces. Three dimensional information of different scans of the same object may also be merged after determining lines or planes tangent to a surface at a discrete number of points and performing registration and merging.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 14/099,199, filed Dec. 6, 2013, which is a continuation of U.S.patent application Ser. No. 12/371,473 filed. Feb. 13, 2009, now U.S.Pat. No. 8,605,989, the disclosures of which are incorporated byreference herein.

BACKGROUND OF THE INVENTION

The present invention relates generally to three dimensional objectanalysis, and more particularly to object recognition using threedimensional information.

Three dimensional scanners are used in a wide variety of applications.Such scanners may be used as part of an engineering design process, forexample to capture information of a prototype design, a manufacturingprocess, for example to capture shape information of manufactured part,and in a wide variety of medical or security-related applications.

Determining if results of different scans represent the same object orif a known object has changed between scans, however, may be difficult.

BRIEF SUMMARY OF THE INVENTION

The present invention provides for object recognition and fusing,mosaicing, or supplementing of three dimensional model information of anobject.

In one aspect the invention provides a method using a computer ofdetermining congruence between physical objects, the physical objectseach having a surface described by a model, comprising: determining, fora model of a first physical object, a first plurality of tangencypoints; determining, for the model of the first physical object, a firstplurality of lines coupling tangency points that do not intersect asurface defined by the model of the first physical object in a vicinityof the tangency points coupled by the first plurality of lines;determining, for a model of a second physical object, a second pluralityof tangency points; determining, for the model of the second physicalobject, a second plurality of lines coupling tangency points that do notintersect a surface defined by the model of the second physical objectin a vicinity of the tangency points coupled by the second plurality oflines; registering the model of the first physical object and the modelof the second physical object to a common coordinate system using thefirst plurality of lines and the second plurality of lines; determininga measure of discrepancy between the model of the first physical objectand the second physical object; and declaring that the first physicalobject is the same as the second physical object if the measure ofdiscrepancy is less than a predefined magnitude.

In another aspect the invention provides a method using a computer ofdetermining if a first physical object is the same as a second physicalobject, comprising: receiving a model of a first physical object and amodel of a second physical object, the model of the first physicalobject comprising a plurality of points descriptive of a surface of thefirst physical object and the model of the second physical objectcomprising a plurality of points descriptive of a surface of the secondphysical object; determining n-tangents for the model of the firstphysical object and the model of the second physical object; determiningif aspects of the surface of the first model and aspects of the surfaceof the second model match within a predefined criteria; and declaringthat the first physical object and the second physical object are thesame physical object if the corresponding n-tangents match within thepredefined criteria.

In another aspect the invention provides a computer system configured todetermine groupings of points of tangency for models of physicalobjects, comprising: at least one memory containing program instructionsand information defining a surface a physical object using a pluralityof points; and a processor configured by the program instructions to:determine lines coupling pairs of points; for each line coupling pairsof points determine if the line cross the surface of the physical objectabout either of the pairs of points; and selecting lines coupling pairsof points that do not cross the surface of the physical object abouteither of the pairs of points.

These and other aspects of the invention are more fully comprehendedupon review of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a scanning and processing system in accordance withaspects of the invention.

FIG. 2 shows a visual representation of results of a scan and a furtherrepresentation of results of a scan showing a tritangent plane.

FIG. 3 shows a flow chart of a process for determining if scans ofobjects are scans of the same object.

FIG. 4 shows a flow chart of a further process for determining if scansof objects are scans of the same object.

FIG. 5 shows a flow chart for determining n-tangents.

FIG. 6 shows a flow chart for determining registration errors.

FIG. 7 illustrates a triangle and two surfaces in a coordinate systemwith respect to determination of registration errors.

FIG. 8 shows a flow chart of a process for fusing, mosaicing orsupplementing information of two scans of the same object.

DETAILED DESCRIPTION

FIG. 1 shows a scanning system for obtaining three dimensionalinformation of an object 111. A three dimensional scanner 115 obtainsthree dimensional information of an object, generally by scanning theobject. A number of three dimensional scanners are commerciallyavailable, and the three dimensional scanners may operate as astandalone device or in conjunction with a computer unit, for examplediscussed below, executing software generally provided by the threedimensional scanner vendor. In many embodiments the scanner obtainsinformation about location in space of a plurality of points of theobject. In many embodiment the points of the object are points on asurface of the object, although in some embodiments the points of theobject may be points within an object, generally depending on the typeof scanner.

The information about location in space of the plurality of points ofthe object is provided to a computer unit 117 coupled to the scanner,although in some embodiments the computer unit and three dimensionalscanner may share a common housing or elements of the computer unit andthree dimensional scanner may share some or all of a plurality ofhousings. The information about location in space of the plurality ofpoints of the object may be in the form of data, for example distanceand angle from a scanning device to each of the plurality of points onthe object, with the computer unit for example determining informationof a three dimensional model of the object. Alternatively, theinformation about location in space of the plurality of points may be inthe form of information of a three dimensional model of the object. Thethree dimensional model of the object may be, for example for a surfaceof the object, in the form of a point cloud, with a plurality of pointsidentified by location in a coordinate system The three dimensionalmodel of the object alternatively may be, again for example for asurface of the object, in the form of a three dimensional mesh, withlocation and orientation of a plurality of polygons identified. In manysuch instances the polygons are planar triangles, and the location andorientation of the plurality of triangles is provided by way ofidentifying location of vertices of the triangles in a coordinatesystem. In many instances a graphic display device associated with thecomputer unit may, in conjunction with graphic display related circuitryof the computer unit, display representations of scans, and FIG. 2 showsa visual representation 211 of result of a scan.

The three dimensional scanner may also perform a second scan of afurther object, to obtain information of a further three dimensionalmodel. The further object may or may not be the same object as theobject. In some embodiments the second scan is performed by a scannerother than the scanner 115.

The computer unit processes information of the three dimensional modeland the further three dimensional model. In many embodiments thecomputer unit determines, based on the processing of the information,whether the three dimensional information and the further threedimensional information are models of the same object, namely that thescanned object and the scanned further object are the same object. Insome embodiments, the computer may fuse, mosaic, or supplement threedimensional model information. For example, one set of three dimensionalmodel information may be supplemented with information of the other setof the three dimensional model information, or the sets of threedimensional model information may be combined so as, for example, toprovide more complete three dimensional model information.

FIG. 3 is a flowchart of a process for determining if objects are thesame in accordance with aspects of the invention. The process may beperformed, for example, by the system of FIG. 1, or a computer unit ofthe system of FIG. 1. In block 311 the process receives sets of threedimensional model information. At least two sets of information arereceived, with the sets of information being for the same or differentphysical objects. In most embodiments each of the sets of threedimensional model information are generated, at least in part, byscanners scanning three dimensional objects. In some embodiments each ofthe sets of three dimensional model information are representative of asurface of a head or portions of a head of person. In other embodimentsthe sets of three dimensional model information are representative ofsome other object, or may be information representative of items withina volume of an object, for example organs or other items within a bodyof a person. As indicated above, the three dimensional model informationmay, for example, define a plurality of planar polygons, generallytriangles, forming a mesh indicative of a surface, or may, for example,be in the form of a point cloud with, in various embodiments, the pointcloud being a volume point cloud or a surface point cloud.

In block 313 the process determines corresponding tangent lines orsurfaces for different sets of the three dimensional model information.The tangent lines are, for each set of three dimensional modelinformation, lines coupling points on a surface described by the threedimensional model information, with the lines generally tangent to thesurface described by the three dimensional model information. In manyembodiments it is sufficient if the tangent lines are only generallytangent to the surface in the vicinity of the points, which may at timebe referred to as tangency points. Similarly, tangent surfaces are, foreach set of three dimensional model information, defined by intersectingtangent lines. A tangent line couples two tangency points, a tangentsurface, for example a tangent triangle, couples three tangency points.In some embodiments the number of coupled tangency points in the sameplane is user defined, and may include two, three, or more tangencypoints, and may be considered an n-tangent, n greater than or equal totwo. In addition, in some embodiments the three dimensional modelinformation may be information simply of surfaces. In other embodimentsthe three dimensional model information may, for example, associate abrightness or color or other information with points in the model. Insuch instances edges of level sets of brightness or color, for example,may be used to define surfaces, some of which may be interior, of thethree dimensional model information.

In some embodiments tangency points used to create n-tangents arerestricted to tangency points that are distant from one another by apredefined, or in some embodiments adjustable, distance. Limiting theuse of tangency points to those points greater than a minimum distancefrom one another is beneficial, for example, in avoiding selection ofadjacent or nearly adjacent points for use in forming n-tangents, as useof such points may provide insufficient information regarding a surfaceof an object. In some embodiments the minimum distance may be, forexample, 100 times the average distance between adjacent points in thethree dimensional model information.

In some embodiments corresponding n-tangents between three dimensionalmodel information may be determined. Corresponding n-tangents arecomprised of tangent lines or surfaces with similar attributes. Forexample, corresponding tangent lines may be selected on the basis ofsimilar lengths, and corresponding tangent triangles may be selected onthe basis of similar area, similar angles for interior angles of thetriangles, or similar lengths of some or all of the lines forming thetriangles. In some embodiments the process determines that there are nocorresponding n-tangents, and the process declares that the physicalobjects represented by the different sets of three dimensional modelinformation are different objects. Similarly, in some embodiments theprocess, after determining corresponding n-tangents, declares that thephysical objects represented by the different sets of three dimensionalmodel information are the same object. In such embodiments the processmay thereafter return, without performing further operations.

In block 315 the process determines discrepancies, which may beconsidered errors, between n-tangents, for example correspondingn-tangents. In most embodiments the errors between correspondingn-tangents relate to a measure of differences between the n-tangents andthe corresponding surfaces in the three dimensional model information. Alarge variety of error constructs may be used. The error constructs maybe in the form of a correlation measure, a global measure, or some othermeasure. For example, in some embodiments the process determines errorsbetween corresponding n-tangents by comparing differences in areas, forthe case of n equal to 2, or volumes, for cases where n is greater than2, between the n-tangents and surfaces of the objects, with the surfacesas defined by the sets of three dimensional model information. In someembodiments a representation of the differences in area or volume aredetermined. For example, in many embodiments a number of discrete pointson each n-tangent are selected, a distance between the point and thecorresponding surface is determined, the distances are summed for eachobject, and differences in the summed distances are determined. In someembodiments the representation of the differences in area or volume isdetermined with respect to the number of discrete points used, with thedistances are divided by the number of discrete points to provide anaverage distance in representation of area or volume, and differences inthe average distances are determined. Other examples of determination oferrors between corresponding n-tangents are also described later herein.In addition, in some embodiments errors between corresponding n-tangentsmay be determined by comparing errors between pairs of n-tangents, withone n-tangent of a pair for one three dimensional models and the othern-tangent of the pair for the other of the three dimensional models,and, for example, using the pairs with the lowest errors ascorresponding n-tangents.

In block 317 the process determines if the errors are within apredefined amount. If so, the process proceeds to block 319 and declaresthat the sets of three dimensional model information are for the sameobject. Otherwise the process proceeds to block 321 and declares thatthe sets of three dimensional model information are for differentobjects. In either case, the process thereafter returns.

FIG. 4 is a flowchart of a further process of determining if objects arethe same in accordance with aspects of the invention. In block 411 theprocess finds tritangent planes, or in many embodiments simplytritangent triangles, for two representations of surfaces (which in someembodiments may be interior surfaces) of three dimensional physicalobjects, which may or may not be the same physical object. An example ofa tritangent plane 213 for a visual representation 215 of results of ascan is shown in FIG. 2. Each of the representations of threedimensional physical objects may comprise data indicating a point cloudrepresentation, or may comprise data indicating polygons, usuallyplanar, in space forming mesh representation of the physical objects. Inmany instances the planar polygons are planar triangles.

In some embodiments the process determines tritangent planes for each ofthe representations by determining three planar polygons that are,within some range, coplanar, namely with the planar polygons sharing,within some range, the same plane. In some such embodiments the planarpolygons are declared coplanar if the planes of the polygons are withina predefined distance of one another, or if an angle of intersection ofthe planes of the polygons is smaller than a predefined amount. Further,in some embodiments the three planar polygons must also be greater thana predefined distance from one another. In some embodiments the processfirst determines two planar polygons that share a common plane, whichmay be considered bitangent lines or bitangents, and then determines athird planar polygon that also shares the common plane.

In some embodiments the process determines bitangents by consideringstraight lines that connect pairs of tangency points of the object, andselecting such straight lines that do not cross the surface of theplanar polygons in the vicinity of the tangency points. In someembodiments planar polygons are determined using points of a point cloudrepresentation. In some embodiments a manifold, representative of asurface of the object, or a surface ikn the vicinity of the tangencypoints is determined, with manifolds used in place of the polygons. Insome embodiments the distance between the tangency points should begreater than a predefined distance. The process then determines if twodifferent bitangents share a common tangency point, if so tangencypoints of the two bitangents form a triangle, and the triangle may bereferred to as a tritangent or tritangent triangle.

In some embodiments block 413 is performed, although in some embodimentsoperations of block 413 are omitted. In block 413 the process determinesif tritangents of the different representations are similar. In someembodiments tritangents are considered similar if they have a similarattribute. In some embodiments tritangents are considered similar ifthey have similar areas, for example areas that differ less than apredefined amount or percentage. In some embodiments tritangents areconsidered similar if, for example, for a first tritangent formed ofpoints ABC and a second tritangent formed of points DEF|AC|/|AB|=alpha*|DE|/|DF|, with alpha some value approximately equal to1.

In block 415 the process determines if similar tritangents were found.If not, the process goes to block 421 and declares that the threedimensional physical objects are different objects, and returns.Otherwise the process goes to block 417.

In block 417 the process determines an error between tritangents, thesimilar tritangents if operations of block 413 were performed. In someembodiments the process determines an error between similar tritangentsby determining a difference between an average distance betweencorresponding points in both tritangents. In some embodiments theprocess determines an error, for triangles ABC and EPG, by using atransformation to map the triangles to a common plane, using the sametransformation for surfaces of the three dimensional information of theobjects, selecting points within the triangles, determining distancesfrom the points to the surfaces, the distances being in a directionorthogonal to the planes of the triangles, and determining a differencebetween average distances for the points.

Accordingly, in some embodiments, for triangles ABC and DEF, A and D aremapped, generally by translation to an origin of an x-y-z coordinatesystem, vectors AB and DE are aligned, generally by rotation, with apositive axis of an x-axis of the coordinate system, and each triangleis rotated until points C and F are in the x-y plane. The sametranslations and rotations are performed for the surface of the threedimensional information of the objects.

Each of the triangles are discretized. The triangle may be discretizedusing, for example, a rectangular grid. Alternatively, areas outside thetriangles may be discretized, or areas about the tangency points. Insome embodiments only discretization points that, based on their x-ycoordinates, would be within both triangles are used, providing Ndiscrete points for each triangle. For each discrete point a distance,in the z-direction, is determined to the corresponding surface. In someembodiments the sum of the difference in distance between correspondingdiscretization points, divided by the number of discrete points isdetermined as a registration error. As indicated above, a number ofmeasures of error, or discrepancy, may be used. For example,alternatively a maximum of the differences in distance may be determinedas the error, or the differences may be computed with respect tofrequency domain representations of each data set.

In some embodiments the discrete points are chosen such that distancebetween the discrete points is related to the average distance betweenneighboring points in the three dimensional mesh information, forexample the distance between discrete points may be selected to be thesame as the average distance between neighboring points in the threedimensional mesh information.

In block 419 the process determines if the error is less than some valued. In many embodiments d may be or may be based on an average distancebetween points in a point cloud or points in a three dimensional mesh.If the error is less than d, the process proceeds to block 423 anddeclares the physical objects to be the same. If not, the processproceeds to block 421 and declares the physical objects to be different.In either case the process thereafter returns.

FIG. 5 is a flow chart of a process for determining n-tangents inaccordance with aspects of the invention. In block 511 the processdetermines barycenters and planes for polygons of a mesh describingsurfaces of a three dimensional object. In some embodiments the processis provided barycenter information for polygons of the mesh, with inmost embodiments the polygons forming triangles with the barycenterswithin the triangle, along with apex positions of the triangles within acoordinate system.

In block 513 the process determines polygons with the same plane. Insome embodiments two polygons are considered to have the same plane ifan angle between the two planes is less than a threshold, for example auser defined threshold.

In some embodiments a mesh describing a surface of an object is formedof triangles, and may include n triangles. In such embodiments, eachtriangle may be identified as T_(i), with I=1 . . . n. Triangles withthe same plane may be determined by considering, for each triangleT_(i), all triangles T_(j), j>I, with distances from a barycenter ofT_(i) to a barycenter of T_(j) greater than a user defined threshold, ora threshold based on average distances between barycenters (for example50 times the average distance between barycenters), or some otherdistance. For all such triangles T_(j), T_(j) is coplanar with T_(i) ifthe distance from the barycenter of T_(j) to the plane of T_(i) is lessthan a predefined distance and an angle between a plane of I; and aplane of T_(i) is less than a predefined angle. In some embodiments thepredefined angle is ten degrees.

In block 515 the process determines n-tangents defined by barycenters ofn polygons having the same plane. In some embodiments a mesh describinga surface of an object is formed of triangles, and may include ntriangles. In such embodiments a tritangent, for example, may bedetermined by performing the operation described for such embodimentswith respect to block 513, but using triangle T_(j) in place of triangleT_(i), and determining a further triangle T_(k), with k>j.

The process thereafter returns.

In some embodiments a cloud of points describing a surface of an objectmay be used instead of triangles. In such embodiments bitangent linesmay be determined by, for all pairs of points, determining a linesegment passing through the pair of points, determining a planeincluding one of the points and normal to the line, selecting pointsnear one of the pair of points and selecting points near the other ofthe pair of points, projecting the selected points to the plane,determining vectors from the one of the points included in the plane andthe projected points, and determining if the maximum angle between anytwo of the vectors is less than 180 degrees. N-tangents may be similarlydetermined, for example by repeating the above, or by determiningbitangent line segments that intersect, or for a third point,determining a plane including the pair of points and the third point anddetermining if all of the points near the pair of points and the thirdpoint are on the same side of the plane. In some embodiments points nearthe pair of points may be determined by determining if the points arewithin a predefined distance of either of the pair of points or forminga region of planar polygons, for example having vertices of points,about the pair of points and determining points that are part of apolygon within a number of polygons, for example within neighboringpolygons, about either of the pairs of points, or some other measure.

FIG. 6 is a flow diagram of an embodiment of a process for determiningregistration errors for tritangents in accordance with aspects of theinvention. In block 611 the process aligns triangles formed of thetritangents. In many cases the position of triangle apexes of thetritangents, for example, may have different locations in coordinatesystems of the three dimensional model information from which eachtritangent is derived. Aligning triangles, along with performing thesame transformation done with respect to alignment of triangles forother information of the three dimensional model information, can bothallow for easier processing for determination of registration error andlargely register both sets of three dimensional model informationsubstantially in the same coordinate system.

In some embodiments alignment of triangles is performed by translating afirst apex of each triangle to an origin of an x-y-z coordinate system.A first leg of each triangle, extending from the first apex, is thenrotated, if necessary, to align with an x-axis of the coordinate system.A second leg of each triangle, also extending from the first apex, isrotated to lie in an x-y plane of the coordinate system. In someembodiments, more generally an affine transformation is applied to thefirst triangle to position the first triangle as discussed above, and anaffine transformation is applied to the second triangle to place thesecond triangle in the same position as the first triangle. The sametransformation, of translations, rotations, and possibly zooms, isperformed for other information for each of the three dimensional modelinformation.

In block 613 the process selects a number of discrete points of eachtriangle. In some embodiments each of the discrete points is separatedby a predefined distance. In some such embodiments it has been founduseful to have the predefined distance be the same as the averagedistance between points in the three dimensional model information, orthe average distance between barycenters of polygons of the threedimensional model information. Accordingly, in some embodiments theprocess selects discrete points across the surface of each triangle suchthat each discrete point is separated by the predefined distance, withas many discrete points used as may be selected within the surface ofthe triangle that meet this criteria.

In block 615 the process determines corresponding surface points of eachof the transformed three dimensional model information for each of thediscrete points. Each of the corresponding surface points have the samex and y values of corresponding discrete points, but may have differentz values.

In block 617 the process determines a registration error between thesurfaces of the transformed three dimensional model information. Foreach of the discrete points the registration error is the distance, inthe z-direction, between corresponding points of the two surfaces. Anexample of a registration error for a particular discrete point is shownin FIG. 7. In FIG. 7 a triangle ABC and a triangle A′B′C′ are shown inan x-y plane of an xyz coordinate system. A plurality of discrete pointsare within the triangles. A surface 1 and a surface 2 are shown abovethe x-y plane, although it should be recognized that the surfaces willgenerally be tangent to the x-y plane at points A, B, C (which alsocorrespond to A′, B′, C′). A point P1 on surface 1 is a correspondingpoint for a particular discrete point i,j, and a point P2 on surface 2is also a corresponding point for the particular discrete point i,j. Aregistration error for the particular discrete point i,j is a distancee_(ij) between point P1 and point P2. It should be noted, however, thatin some embodiments points outside the triangle are included, and insome embodiments only included, in the plurality of discrete points.

In some embodiments a total registration error is determined, namely thesum of the registration error for each of the discrete points. However,it is generally useful to instead determine an average registrationerror, for example the sum of the registration error for each discretepoint divided by the number of discrete points, or a median or maximumregistration error or some other type of registration error. Asindicated above, however, a variety of different characterizations ofregistration error may be used.

The process of FIG. 6 thereafter returns.

FIG. 8 is a flow chart of a further process in accordance with aspectsof the invention. The process of FIG. 8 fuses, generates a mosaic of orsupplements three dimensional information, generally from separate threedimensional model information of the same physical object but in someembodiments from three dimensional model information of differentphysical objects. For a variety of reasons, three dimensional modelinformation generated by a scanning device may not frilly generateinformation for a surface or a volume of an object, leaving holes orgaps within the information.

In block 811 the process determines n-tangents for three dimensionalinformation generated by scans of the same physical object. In manyembodiments the process determines n-tangents as discussed herein, forexample by determining tritangent triangle based on tangency points.

In block 813 the process determines a transform (or a transform for eachscan) to map information from one (or more) of the scans to informationof a single scan, or, more generally, to map information from the scansto a common coordinate system. Again, determination of the transform maybe performed as discussed herein. In many embodiments the transform is arigid transform, although in some embodiments a non-rigid transform maybe used.

In block 815 the process merges data of the scans. In many embodimentsmerging of data of the scans is performed by applying the transform topoints in the scans to a common coordinate system. In some embodiments,the merged data is additionally filtered or smoothed, for example, toreduce noise or effects of inconsistencies in the merged data. Forexample, in some embodiments, local or near data points are averaged, orthe merged data may be or tessellated, for example using cubes, andpoints within each cube are assigned an average position of pointswithin the cube. The process thereafter returns.

In some embodiments of the invention other or an additional process oradditional processes are performed to transform three dimensionalinformation to a common coordinate system. In some embodiments localcurves from each of the sets of three dimensional model information areextracted, the local curves are encoded, meaningful matches aredetermined between the local curves, and a transform to map local curveswith meaningful matches, or local curves with the most meaningful match,is determined.

In some such embodiments tritangents for two sets of three dimensionalinformation are determined, and intersections between the additionalplanes and surfaces of the three dimensional information are determined.The additional planes may be planes parallel to planes defined by thetritangents, offset by a selected distance d, or may be planes formingan angle with planes defined by the tritangents and intersecting a sideof a triangle formed by the tritangents. In some embodiments thedistance d is related to an aspect of, for example, a tritangent area,with d having the same relation to tritangent area for each tritangent.Preferably the additional planes are selected such that the intersectionwith the surfaces of the three dimensional information are Jordancurves.

The curves are encoded using a similarity or affine invariant encoding,with in most embodiments similarity encoding being used. Meaningfulmatches are determined for corresponding curves, and a geometrictransform mapping one of the corresponding curves to the other, ortransforms mapping both to common positions in a common coordinatesystem, is determined. Points of the three dimensional modelinformation, or barycenters in the case of three dimensional modelinformation comprised of polygon information, are transformed using thetransformation, preferably for each of the geometric transforms. Ameasure of meaningfulness is associated with clusters of points for eachof mappings, and a transform with the most meaningful clusters isselected for transforming information of the three dimensional modelsfor further processing, for example for computing registration errors.

Although the invention has been described with respect to specificembodiments, it should be recognized that the invention may be practicedother than as specifically described. Accordingly, the inventioncomprises the novel and unobvious claims and their insubstantialvariations, supported by this disclosure.

The invention claimed is:
 1. A method using a computer of determiningcongruence between physical objects, the physical objects each having asurface described by a model, comprising: determining, for a model of afirst physical object, a first plurality of tangency points;determining, for the model of the first physical object, a firstplurality of lines coupling tangency points that do not intersect asurface defined by the model of the first physical object in a vicinityof the tangency points coupled by the first plurality of lines;determining, for a model of a second physical object, a second pluralityof tangency points; determining, for the model of the second physicalobject, a second plurality of lines coupling tangency points that do notintersect a surface defined by the model of the second physical objectin a vicinity of the tangency points coupled by the second plurality oflines; registering the model of the first physical object and the modelof the second physical object to a common coordinate system using thefirst plurality of lines and the second plurality of lines; determininga measure of discrepancy between the model of the first physical objectand the second physical object; and declaring that the first physicalobject is the same as the second physical object if the measure ofdiscrepancy is less than a predefined magnitude.
 2. The method of claim1 wherein the first number of tangency points is 3 tangency points, thefirst number of lines is 3 lines, the second number of tangency pointsis 3 tangency points, and the second number of lines is 3 lines.
 3. Themethod of claim 2 wherein registering the model of the first physicalobject and the model of the second physical object to a commoncoordinate system using the first plurality of lines and the secondplurality of lines comprises determining a transform to place a firsttriangle formed by the first plurality of lines to a position in acoordinate system, determining a transform to place a second triangleformed by the second plurality of lines to the position of the firsttriangle, and transforming points of the model of the first physicalobject.
 4. The method of claim 3 wherein the first transform is a nulltransform.
 5. The method of claim 3 wherein determining a measure ofdiscrepancy between the model of the first physical object and thesecond physical object comprises determining a measure of differences inposition of at least some corresponding points of surfaces of thetransformed first model and the transformed second model.
 6. The methodof claim 5 wherein the at least some corresponding points areapproximate the first triangle or the second triangle.
 7. The method ofclaim 1 further comprising merging information of the first model andinformation of the second model.
 8. The method of claim 1 whereinregistering the model of the first physical object and the model of thesecond physical object to a common coordinate system using the firstplurality of lines and the second plurality of lines comprises:extracting first local curves from the model of the first physicalobject by determining intersections with a surface defined by the modelof the first physical object and a plane associated with the firstplurality of lines; extracting second local curves from the model of thesecond physical object by determining intersections with a surfacedefined by the model of the second physical object and a planeassociated with the second plurality of lines; encoding the first localcurves and the second local curves determining meaningful matchesbetween the local curves; determining a first transform to map the firstlocal curves with meaningful matches and a second transform to map thesecond local curves with meaningful matches to a common position on acoordinate system; and applying the first transform to information ofthe model of the first physical object and applying the second transformto information of the model of the second physical object.
 9. The methodof claim 8 wherein the first local curves and the second local curvesare Jordan curves.